Josephson Junction-Based Compact Notch Purcell Filters for Superconducting Qubit Readout

High-fidelity qubit readout in circuit quantum electrodynamics (QED) requires suppressing relaxation due to the Purcell effect, typically achieved through the use of Purcell filters. A key limitation of existing Purcell filter implementations is their large footprint. In this work, we propose a compact notch Purcell filter based on a Josephson junction chain embedded in series with the readout resonator. We analytically derive the conditions for operation in the dispersive regime using a lumped-element model, and validate the concept through an example design that is analyzed through both lumped-element and full electromagnetic simulations. The results indicate that the proposed architecture achieves a Purcell decay time exceeding 1 ms, with a dispersive shift and resonator linewidth of approximately 10 MHz, enabling fast, high signal-to-noise ratio readout. As typical of notch filters, also this solution exhibits an inherent parameter sensitivity. Superconducting quantum interference device (SQUIDs) can be used for postfabrication frequency tuning, at the expense of an increase of the number of required control lines.